Synchro to digital converter



May 10, 1966 s. F. scHRoEDER ETAL 3,250,905

SYNCHRO TO DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Shea?I 1 :ffl-3.1

INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE BY M@ ATTORNEY May 10, 1966 G. F. scHRoEDl-:R ETAL 3,250,905

SYN'CHRO TO DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Sheet 2 mmm www. www vhw.

INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE BY YL/(016,( f ATTORNEY May l0, 1966 G. F. scHRoEDER ETAL 3,250,905

SYNCHRO TO DIGITAL CONVERTER original Filed Feb. 1o. 1961 9 sheets-sheet s m m wx R5@ NSN@ WMM V H R @Qns m/wwm mwww Q xmm @uw u@ WQSQIF n m M F. Y. .ww oo. mm om mm om Q Q n QT m w R A O N @l m IIIIIIIIIIIIIIIIIIIII'IIIII I l I I I I I I l l I I @NI l N \\\\|f\ QI N l l |....l l l@ NI l llllL Wmw Wkmwwmm, Nmwxmmmm xmmm Q m.; m. Aww. RGS 66% \VGQ\ 90N BQ kmh, mm. EN RSN May 10, 1966 G. F. scHRoEDER ETAL 3,250,905

SYNCHRO To DIGITAL CONVERTER Original Filed Feb. l0, 1961 9 Sheets-Sheet 4.

All .d NNN wmm NNN INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE ATTORNEY MY 10, 1966 G. F. scHRoEDER ETAL 3,250,905

SYNCHRO TO DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Sheet 5 een( 25K 50K /OOK 200K 400K 600K 25K 50K /OQK '05 /OT/JA/ /0 Jj' 55K 00320' 'VVV 25K 5K 25K 50,4/ foo/f 200K 400K 800K 25K .T- 251( 50K 800K co5 edm/20 @47 /205K /MK 25K ok /00K 200K 400A/ 800K /205K 25K ma# 40o/ .Q05 3dr/W30 ,xga

5.3K co5 4o /205K 251( 93;( 25K wk loo/K i200# 400i( 800i( w05# 25K 95H 25K T T 40o/f ook INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE ATTORNEY May 10, 1966 G. F. scHRoEnER ETAL 3,250,905

SYNCHRO TO DIGITAL CONVERTER INVENTORS SCHROEDER RONALD Y. ZARADISE By ff @VTM @NAW @nf Qw M w w W W ...Sq

ATTORNEY May 10, 1966 G. F. scHRoEDER E'rAL 3,250,905

SYNCHRO TO DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Sheet '7 May 10. 1966 G. F. SCHROEDER ETA.. 3,250,905

SYNCHRO TO DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Sheet 8 INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE ATTORNEY May l0, 1966 G. F. scHRol-:DER ETAL. 3,250,905

SYNCHRO T0 DIGITAL CONVERTER Original Filed Feb. 10. 1961 9 Sheets-Sheet 9 COMP/M7470@ 4MB/6 w TY CTOR D675@ TOR M4 TQ/X INVENTORS GEORGE F. SCHROEDER RONALD Y. PARADISE BY ,may f5 ATTORNEY United States Patent O 3,250,905 SYNCHRO T DIGITAL CONVERTER George F. Schroeder, Wayne Township, and Ronald Y.

Paradise, Hillsdale, NJ., assignors to General Precision Inc.,Little Falls, NJ., a corporation of Delaware Original application Feb. 10, 1961, Ser. No. 88,330, now

Patent No. 3,071,324, dated Jan. 1, 1963. Divided and this application Mar. 15, 1962, Ser. No. 186,814

Claims. (Cl. 23S-197) This is a division of application Serial No. 88,330, tiled February 10, 1961, now patent No. 3,071,324 which was granted January 1, 1963.

The present invention relates to an angle readout, and more particularly to the furnishing of an angular position from information derived from a synchro or resolver.

Rotating devices furnishing angular information are widelyused in computer circuitry. Typical of such devices now in common use are synchros and resolvers. These devices will furnish the sine and cosine of an angle. The synchro in its simplest embodiment includes a transformer primary and a Y-shaped secondary winding. One winding is movable with respect to the other in response to some motion or input.v The angular position of the Y-shaped secondary with respect to the primary provides output voltages which can be used to obtain the sine and cosine of the angle. Although for some computer operation no angle readout is required, in other operations, it is advantageous to have a rapid angular readout. Attempts have been made to introduce this feature by various methods, eg., by measuring pulse time between zero crossings. This however introduces numerous complications in the circuitry and is subject to distortion and error. Reading the angle directly from the sine or cosine presents certain difiiculties as neither the sine nor the consine functions exhibit suficient linear characteristics to provide a readily convertible angular readout. Although attempts may have been made to provide a rapid angular readout directly from a synchro or resolver, none, as far as we are aware have ever been too successful when put into practice in actual operation.

It has now been discovered that an angular readout from a synchro or resolver can be readily provided.

Thus, it is an object of the present invention to provide readable angular information.

Another object of the present invention is to provide an angular readout from a synchro or resolver.

Still another object of the present invention is the construction of a network which will provide a monotonic increasing function, or decreasing function.

Yet another object of the present invention is to provide the foregoing results by means of a ratio effect between the sine and cosine outputs so as to operate from almost any input voltage or frequency.

The present invention also contemplates providing an arrangement whereby an electrical circuit may furnish electrical values corresponding to desired mathematical functions.

With the foregoing and other objects in view, the inven-A ice 45 into which is fed one of the outputs from a sine-cosine source, e.g., from a synchro or resolver; overload switch means allowing only electrical values through said network which are less than values flowing thereto; and, comparator means into which is fed the other of the outputs from said source and the output from said network.y The particular arc of the circle in which the angle sensed by the source is located will be supplied by logic means.

The advantages of the invention will become apparent from the following description taken in conjunction with the accompanying drawing in which:

FIGURE l shows schematically a portion of the switchresistor network herein contemplated used in connection with the coarse or base angular binary positions;

FIGURE 2 shows schematically a portion of the switch- -resistor network herein contemplated used in connection with the fine angular values;

FIGURE 3 is a schematic and mathematical illustration of the assembled base and fine angular binary position resistor branches and the attenuation network interrelating the base and ne branches;

FIGURE 4 is a block diagram of the operation of the switch resistor network contemplated herein;

FIGURE 5 shows schematically the switch-resistor network depicted in FIGURE 4; v

FIGURE 6 gives the electrical resistor equivalent net-v work corresponding to the theoretical 10 readout;

FIGURE 7 gives the electrical resistor equivalent network corresponding to the theoretical 20 readout;

FIGURE 8 gives the electrical resistor equivalent network corresponding to the theoretical 30 readout;

FIGURE 9 gives the electrical resistor equivalent network corresponding to the theoretical 40 readout;

FIGURE 10 shows in graph and symbol form the eight octants of a circle, the position of the sine and cosine in each octant, and the phase of the cosine with respect to .the signal reference, i.e., phase of the cosine secondary with respect to the excitation primary signals;

FIGURE ll gives in block diagram the units required in connection with octant selection;

FIGURE 12 is a detailed schematic diagram of the conversion system given in block diagram in FIGURE ll;

FIGURE 13 shows in block diagram the sector or octant selection when there is both a coarse input and a line Vernier input; and

FIGURE 14 is a graph of an error curve for a tangent readout obtained in accordance with the invention herein contemplated.

To describe the construction of the device herein contemplated, it is first necessary to visualize the mathematical principles involved. Once the mathematical fundamentals have been grasped, the construction of the device in actual practice will be clearer.

Some synchro assemblies use coarse and fine synchros. The fine synchro acts as a vernier and turns at a speed which is a multiple of that of the coarse synchro. A fine reading` is thus obtainable within the angle obtainable from the coarse synchro. To simplify the explanation of the invention, the initial part of the description is not concerned with coarse or fine sync-hos. Rather, it is assumed that there is a device, e.g., a resolver which furnished only the sine-cosine of an angle and from this information, the angle itself is to be obtained.

The present invention uses a ratio effect. By using a ratio effect, all that is required is the proper initial turns ratio of the input transformers to furnish values corresponding to the sine and cosine and a workable input of voltage and current above a certain threshold.

3 THE CIRCLE AND THE ARCS THEREOF USEFUL FOR THE PURPOSE OF THE PRESENT INVENTION If a circle is divided into binary digits, the following arrangement may be used:

Table 1 Decimal Value Binary Degrees Value NN @aangeslagen Table 2.-Sz'gnfcant tangent and cotangent values Base Position Binary Degrees Value Tangent lines. The tangent or cotangent is readily obtainable from the sine or cosine since sine =cos 0 tan 0; or sine 0=cos 0/cot 0. Since the currents compared rnust be proportional to the tangent the resistances are made proportional to cotangent values which are used to obtain desiredresults.

The object of the present invention however is not merely to provide an angle fromO to 45 (or 28) degrees, but to provide an angle value between 0 and 360 (or 211). This is a value eight times the 45 (or 28) degree are; i.e., the 0 to 45 (or 28) degree arc for which a values have been given in Table 2 is an octant of 360 (or 211) degrees. To accomplish this, three basic problems must be solved. It is first necessary to determine the angle position within the 0 to 45 (or 28) degree arc. The particular octant in which the angle is located must then be selected. And finally, the information from the coarse and ne synchros (if coarse and fine synchros are used to provide the-sine-cosine information) must be interrelated.

THE 0 TO 45 OCTANT-BASE ANGULAR POSITIONS Preferably the number of sections or sectors into which the basic 45 octant is divided for the purposes of the present invention should t into the binary scheme. It may be 2, 4, 8, etc. In Table 2, four segments have been selected namely, 0 to 111Ag 111r to 22'1/2; 221/2 to 33% and 33% to 45. This sector division is suicient Cotangent for most purposes and the invention ywill be described using these sectors although other binary values could be used for greater or lesser accuracy. Looking at Table 2, it is seen that the cotangent value of 221/2 is about 2.414 and the cotangent value of 111i is about 5.03. These are workable resistor values andin fact for the 221/2 branch a resistance value of 24.1K can be used while in the 11% branch a resistance value of 50K can be used. The reason why a 50K instead of a 50.3K resistance value is used is to pull up the -segment curve. At the moment this point is not too important and will be explained subsequently in connection with the description relating to the error curve of the network. The foregoing resistor values 'have been arbitrarily chosen to give a current scale factor of tan 45=1, corresponding to 1 milliampere, i.e., 1x10-3. The 50K resistor value used in the 1111 branch is thus a fortunate coincidence which facilitates computations.

To obtain the 33% base point in binary, both the 221/2 and the 111A resistor branches must read 1, i.e.,

Using the base positions shown in Table 2, it is possible. v to divide the 0 to 45 tangent curve into four straight The cotangent of 33% is 1.4966 or about 1.5. To obtain this value, the following parallel branch resistor arrangement is needed: 24.1K; 50K; and 186K; i.e.,

A circuit 11, using the foregoing resistor values is shown in FIGURE 1. To facilitate the understanding of the invention, each branch part number is related to the binary value of that particular branch, ie., the 221/2 or 2'1 branch is numbered 27; the 111A or 26 branch is numbered 26. Since 33% is not ia binary, that branch is simply numbered 33. For the present, suiiice it to say that each branch, 27, 26 and 33' of FIGURE 1 is controlled by a switch 27S, 26s and 33s. If an electrical potential corresponding to cos 6 is applied across circuit 11, and current passes only through branch 27, the current value obtained is proportional to cos 6 tan 11%". If both switches 26 and 27 are conducting, then and gate 18 acts on switch 33s to put branch 33 in parallel with branches 26 and 27.

If the digits selected were uniformily incremented between 0 and 45, this would provide a linear interpolation of the angle which would have a high error factor. The present invention incorporates a non-linear interpolation which corresponds moreclosely to the tangent curve,

As a preferred embodiment, the switches shown inv FIGURE 1 are parallel to ground switches as opposed to series switches. Series switches might create noise in the system. To eliminate this noise parallel instead of series switches are used. Instead of only one resistor in each parallel branch, two resistors are used and the switch leading to the ground is placed between the two resistors. For the purposes of the present invention it is preferable that the resistor values on both sides of the switch be of equal value, i.e., 24.1K=12.05K-{-12.05K; 50K=25K +25K; and 186K=93Kl93K- These resistor pairs in parallel branches provide the coarse or base binary positions.

THE 0 TO 45 OCTANT-FINE ANGULAR POSITIONS Fine binary digits shown in FIGURE 2 must be provided and incremented at the proper slope. However, from Table 1, it is apparent that tangent-cotangent values of binary values between 0.17578125 and 5,625 corresponding to the values used for the base binary positions cannot readily be selected. Other values must therefore be selected for the binary values between 20 and 25 for the line angular positions and then the' base and fine values must be interrelated. Since the ne values are not directly -related to the base values, a convenient range must be chosen.

As is evident from Table 2, the tangent curve in the to 45 octant is least linear between 33% and 45. The tine values chosen and the interrelation of the coarse and line values can take this situation into account and, as will ibe shown herein values selected will also correspond to the midpoint in the 33% to 45 arc, i.e., the linear increment will pass through the 3922.5 point.

Remembering that in each branch, two resistors are used with a switch thereinbetween and when any branch is in the network the switch is in the enabling position, While when not in thev network the switch is in the shunted to ground position, if the base resistance value used in the ne branches isR, the total resistance of each branch of the ine values is shown in Table 3.

Table 3.-Fne values 1 Where the highest binary current value is 2m.

But in each branch, there are two resistors of -equal l value totalling to the foregoing values of Table 3.

Therefore, one resistor in any branch n will have a value of 2n RH and the other value of 2n R(1--H) Where 4H is the fractional value of one of the resistors in a branch to the total resistance of the branch.

INTERRELATING BASE AND EINE VALUES IN THE 0 TO 45 OCTANT-33% T0 4:5c

Since a single line segment bet-Ween 33% and 45 tends to provide the greatest tangent to angle error, the tine values are rst interrelated to the coarsevalues in this angle arc. The problem is to select a value for R so as to have a tangent value closely related to 3922.5'. Furthermore, the slope of the line is provided by attenuation between the coarse and ne values.

To calculate the attenuation required to provide the slope of the segment line the values required must first be listed.

Table 4.-Table of values 45 to 33% Angle degrees Decimal Binary I=tan 0 DI 1 digit digit 1 Difference in current value between tau 0 and tan 33%.

Remembering that two resistors are used in each branch and one of these resistors has a value of HR and the other resistor has a value of RIU-H), the conductance into any branch "11 which is shunted to ground or Gnc is The total conductance GT is G n=5 2 n-5 H2n T 'l-yKl-HWR where yn is 1 if the switch in the nth branch is shunted and yn is 0 if the switch in the nth branch is enabling. Therefore,

It we let xn be the opposite of yn, i.c., xn=1 for the switch in the nth branch enabling and xn=0 for the switch The equivalent circuit of the ne netwonkshown in FIGURE 2 is an input Voltage en, a series resistance rs, a shunted to ground resistance corresponding yto all the shunted branches and a parallel in circuit resistance corresponding to all the enabling branches.

Now the voltage V across tine branches 12 of FIGURE 2 is to the total voltage er asthe total impedance of the line `branches Z is to the total impedance Rs-l-Z, or,

Remembering that the cur-rent ilowing at the output point is only the current flowing through the enabling branches, the output is equal to resistance of enabhng branches (i-Hm/eae.

Now the current is the change in output current from X: t0 X11 havm'g Some V'ahle (,Sllee branch er, branches Since the two resistors in each branch are equal, His enabhng In effect therefore l 1S the ademend eur' 1/.. For K we can use the value initially assumed based rent output added to the current output ilowng through 15 upon er being lo Volts making K:1X10 3. the c1rcu1t provldmg values between 33% and 45 Solving now for Rs Hence, from X =0 to X :63 must be proportional to the change in the tangent 0 from the point at the beginning Re 10 32 l l of the arc to the point just before `the end of the arc, i.e., EX 10 3 3(15250) -32568 from 3345 t0 4449.46'. Y 20 63 -From Table 4,

Tangent 3345'=.6681\8 Tangent 4448.46=.99386 Rs=5.3 103 ohms Similarly solving now for VR DI=.32568 6; o Y R 32508K K1`".s256s 103 5"X leg Hence the difference 1n tangent value to be accounted V r for by the yline network in this 33% to 45 arc is .32568, :3o-700-5'3z254Q0K and, f and since, Y z'44..49.40-33 3/4.=.3\256\8K where K is some constant. 32 Now, i4449.40 is the fz' when `all branches are en- 30 R=R iabling or when X=63 and 33 3/4 is the i when no branches are enabling or when X :0. Therefore 63 63 Y R=3-2R.=32 X 25.405 M 0 32568K (1-H)R.+(1-H R' 35 R=50K 32568K=- er v Y The base value of the line branches is thus 50K. RB-l-R The attenuation in series vrequired between 33% and 45 or Rs is 5.3K. R +Rf= e' 4e E ,32568K INTERREMATING BAESLE AND FINE VALUES- And, it is also desired that one of the values provided correspond closely to the midpoint between 33% and 45 or '39 e225. Again lfrom Table 4,

The values required are listed-as in Table 4.

45 Table 5.-Table of values -33% to 221/2" i39'2J25-i33 3/402-15250 but, i39225 is the current only when branch number 25 Angle degrees Deiiel Bliegrty Iztee e Dtgl) or 25 is enabling, i.e., when X :32. Therefore,

35% 04 1 000 000 .0081s .15250K 1)32 /6?e- 50 03 111 1n .68377 .24950 (1. 3 2H R 1 (1 H R, 0 000 000 .41421 .00000 Since as hereinbefore pointed out, The previous DI from Table 4 was .32568. The new DI from Table 5 is .24956. ln addition to the attenuator 32568K: 6r and Rl: @r R v Rs of 5.3K, 4additional attenuation is required. This at- ARs-i-R .32568K e tenuation is provided by a resistor in parallel with the binary network. It is thus necessary to find the Value of and smce H, K and er are values wh1ch lare either known this additional resiston or can be arbitrarily selected, we now have the following 60 NOW, the resistance Value of a resistor is to the toal two equatlons Wlth two unknowns: resistance value of the circuit as the voltage drop across er the resistor is to the total voltage drop in the circuit. 32568K=m (Equmon la) The sum of lall resistors in parallel to provide a current Value of .32568 required in Table 4 is R. If the new at- 15250K= (l-H)32/63e, 65 teliliuation resistorRp ilslplut in parallel with R', the sum of a reslstanc a l 1 H R$ I (1 H)R, esm par e 1s l (Equation 1b) ZR=R1I3D RS and R' can therefore be expressed in terms of H, K 7b and el.. If we let V be the voltage drop across .15250K= 32 .(1 m32/eee' e KR v p 1 63H)R+(1 I1)(.32568K Re) RLHQP 9 (across parallel branches R and Rp); and, if we let E be the total voltage drop in the circuit, i.e., E is the voltage drop across RRs E R R DI s+ (Equation n) Substituting the values given in Tables 4 and 5 and those obtained for Equation II,

Rp=14.378K, value of the resistance required .for attenuation between 33% and 221/2 INTERRELATING BASE AND FINE VALUES- 221/2" TO 11I AND 111/1o TO 0 Using Equation II, and constructing new Tables 6 and 7, the value of the resistance required for attenuation between 2212 to 111i and 11% to 0 can be calculated.

Table 6.-Table of values -221/2" I0 1111 Angle degrees Decimal I=tan DID tan 9 digit Additional resistance value Rp in parallel required for attenuation between 221/2- and 111/4 is RER E (Equation II),

RD :8.148K

Table 7.-Table of values Ill/1 to 0 Y Additional resistance value Rp in parallel required for attenuation between 111A and 0 is TANGENT-COTANGENT SWITCH RESISTOR NETWORK The switch resistor arrangement 10 just described provides values which can be used with the cosine electrical equivalent value to equal the sine equivalent value or which can be used with the sine equivalent value to provide the cosine equivalent value of the angular position. Thus, there is a coarse network 11 for values of 11% (or 26); 221/2 (or 27); and 33% (or 264-27); a iine network 12 gives values between 2 and 25 in the binary code and an attenuation network 13 interrelates the slopes of the increasing digits between 0 and 26; between 26 and 27; between 2'I and 264-27; and between 26-1-2"I and 28. To make the explanation of the network more vivid, the -individual branches, switches, attenuators, and controlling ilip-ops have all been numbered in such a way as to give a clue to their function. Resistor branch 27 is the branch used for an angle of 2230 (or 27); resistor branch 26 is the branch used for the 1115 (or 26) angle, and branches 20, 21, 22, 23, 24 and 25 correspond to the binary values of 2, 21, 22, 23, 24, 25. The switches bear the number of the branch they control and end in s so that switch 27s controls branch 27 and switch 25s controls branch 25. Associated with each switch controlling each branchare tfwo lip-ops. Each flip-Hop likewise bears a number related to the branch it controls. One set of Hip-flops are numbered in the 200 series, the other set in the 300 series. The flip-ilops associated with branch 27 are thus numbered 227 and 327, with branch 22, twe have ip-ops 222 and 322, and with branch 20, we have flip-Hops 220 and 320.

To provide the angle sensed by a synchro, the sine value -providedby the device, i.e., sin 0 is fed to a comparator L14. At this instant, none of the switches in the switchresistor network are enabling and there is no cosine value entering comparator 14, passing through switch-resistor network 10. The output .14a from comparator 14 starts a pulse signal 15. Pulse signal 15 actuates shift register 300 which has a plurality of flip-ops, there being one flipop for each binary branch and it is to be remembered that branch 33 is not a binary branch. Each flip-ilop y 1 1 and shift register. But branch 33 is not a binary branch. The attenuator for the 33% angle, register 133 which has been calculated to have a Value of 5.3K is in series with 'the other branches. Therefore, when any of the coarse binary branches are enabling, the attenuator for that branch is shunted to the ground except of course attenuator 133 which is always in series. Branch 33 does not act alone but in parallel with branches 26 and 27. To accomplish this, a iirst and gate 18 is used. Whenever both branches 26 and 27 are enabling, and gate 18 will place switch 33s in an enabling position, i.e., since it is a transistor switch,` switch 33s will be so biased as to conduct. Whenbranch 33 is thus enabled, attenuators 126, 127 and 100 are shunted to ground. Additional and gates 126g, 127g, and 100g, control attenuators 127, 126, land 100. There are also two inverters, 526 and 527, associated with the three and gates 127g, 126g, and 100g.

The action of the several attenuators with the respective and gates and inverters 526 and 527 is explained in Table 8.

Table 8.-Cntrol of attenaator network Action which takes place Attenua- Coarse tors Angle branches shunted Signal at enabling to Flip Invert and gate ground Ilop Signal by- 33%75 All None 226 1 526 0 1 0 to 22.50 26 126 226 1 526 0 1 0 0 None 100 226 0 526 l 0 1 Table 9.-The0retcal combination-coarse and fine networks Value in D egrc es Branch Binary Number Example I-Angle of .--Upon a sine value being fed to comparator 14, output 14a causes pulse signal 15 to signal shift register 300. A pulse enters the first flipop 327 setting in turn dip-flop 227 in the register 200. Switch 27s is enabled and permits current flow through branch 27 so as to furnish a current weighted for 221/2. This is too high and a second output 14h from comparator 14 fed to flip-flop 227 will bias transistor switch 27s so that branch 27 is shurrted tto gnound. The pulse then passes to flip-flop 326 where exactly the same sequence of events takes place. There is thus a value of Zero in the coarse network. Passing to the line network, the rst flip-Hop set is 325 which in turn sets Hip-flop 225 passing current through branch 25 to give a value of 5.625. Since this v alue is less than the sin 0 value, the signal to the comparator will be reversed in sign, which results in the next pulse allowing switch 25s open and branch 25 remains enabling. The saine happens with branches 24 and 23, both of which remain enabling. At this moment, the folowing value is furnished to comparator 14 through the switch-resistor network 10:

' of .3515625 also too high and finally to branch 20 with a value 01.17578125 likewise too high and the foregoing binary value of 00111000 remains as the value for the 10 angle. The equivalent electrical network to 10 is shown in FIGURE 6.

Example II-Angle of 20.--The steps described for the 10 angle are repeated. The following branches remain enabling:

Total angle value 29.8828125 The equivalent electrical network at 30 is shown in FIGURE 8.

Example IV-A'ngle of 40.-The steps described for the 10 angle are repeated. The enabling branches are:

Branch 33-enabling, but not counted as a binary number 2'I 22.5

Total angle value 39.90234375 The equivalent electrical network at 40 is shown in FIGURE 9.

The values actually obtained in practice are better than the theoretical values demonstrated in the examples. The cotangent values for 111z and 221/2 shown in FIG- URE 1 were 5.0276 and 2.4142 respectively. But resistors corresponding to these Values were not used but instead lower value resistors were used, as will ybe subsequently shown in connection with the error curve, the effect of using these lower values of 50K and 24.1K is to pull up the error curve.

SELECTION OF THE 0 TO 360 OCTANT The angle having been determined within the 0 to 45' are octant, it is now necessary to determine which of eight octants contains the angle.

FIGURE 10 depicts graphically and symbolically what happens during the sine and cosine cycle. As illustrated in FIGURE l0, there are sinusoidal outputs from both the synchro sine and cosine arms. Thus, at any given angle, the sine value of the synchro output may be either positive or negative, dependent on the angle selected. The same can be said of the cosine output.

As the synchro turns through 360 there is a phase shift. The cosine coil turns with respect to the primary input coil so that if there were a unidirectional means and a voltmeter past the cosine input, .the cosine voltmeter would read maximum on one side at swing right to zero at 90 and continue `to maximum on the left -at 180 to swing back towards the right and again reach maximum on the right at 360.

sine has been described as being fed to the switch-resistor network While the sine has been described as going to the comparator. In practice, it is advantageous to feed the highest value of sine or cosine to the switch resistor network with the lower value going to the comparator. The result will be that in octants 2, 4, 6, and 8, the register will provide an angle 6 which is equal to 90-0. In these octants, 0 is obtained by inverting the binary value furnished by the register changing each 0 to 1 and each l to 0 and by the addition of 1 to the least significant digit. A new table incorporating these new factors is given in Table 11.

Table 11 Relative magnitude cos 9 sin 6=0 cos 9 sin H=1 regardless of polarity A-C cycle Polarity of cos 9 Oetant;

Phase of cos 0 to ref.

Inversion of 9 register 0=No 1= Yes 90 29 bit 0= Olf 1=On Examining FIGURE 10, the following statements can be made:

I-The sine and cosine are of opposed polarity in octants 3, 4, 7 and 8,

VII-Irrespective of polarity, the sine is greater than the cosine in octants 2, 3, 6, and 7,

IIL-The phase-ofthe cosine is opposite to the phase of the input primary reference in octants 3, 4, 5, and 6.

Using the foregoing information, a truth table can -he constructed as follows:

Again looking at FIGURE 10, it is evident that the sine and cosine waves shown there corresponding to sin 0 sin wt and cos 0 sin wt really represent only what could be considered one half of a wave envelope. There is another half wave envelope corresponding to sin 0 (sin wt) and cos 0 (sin wt). So far, we have been considering the sine or cosine of the angle information without too much attention being paid to the alternating current instantaneous Value which is Emx sin wt where w=2f t, t being the instant of time at whichthe voltage is measured. The embodiment of the invention herein contemplated however can furnish angle information within microseconds. The A.C. reference voltage may thus be at either half of the cycle, at the instant of comparison.

Furthermore, as the present description is geared to human thinking rather than computer thinking, the co- .switches are open, 407 is closed.

FIGURE 11 illustrates functionally the units required in connection with octant correction matrix 403. The units shown not only indicate the octant but apply the proper signals for conversion, i.e., the sine 0 to cos 0. Polarity detectors 401a and 401b will indicate the signal polarity and always direct that positive signals only be applied to the switch resistor network whether the signal be positive or negative. The magnitude detector 402 will not only 4detect relative magnitudes, but will always direct that the larger of the two signals be applied to the switch resistor network. Information 418 as to the reference and cosine phase are also fed to octant correction matrix 403.

A more detailed schematic diagram of the conversion system is illustrated in FIGURE 12. The cos 0 and sine 6 functions are derived from a scott T transformer configuration which also allows for the required isolation from the three wire synchro 99. The secondary windings on the transformer are center-tapped to allow selection of positive input signals. Considering first the cosine, switches 404 and 405 select the proper input line from the transformer and this input is applied to bufferamplier 406. But, whether sampled or not, the synchro has a constant load by virtue of load controlling switch 407a. The output of the buffer amplifier 406 is fed into a polarity detector 401a which senses a positive or negative signal. Upon detection, switches 404 and 405 are activated, allowing only a positive signal to be fed to buffer amplifier 406. Load controlling switch 407 is controlled by the positions of switches 404 or 405. If either of these two If both are closed, 407 is open. A

The polarity detector consists of a polarity sensor 401e: coupled to a flip-flop 408 through a pulse actuated sequence gating function 409. 'Ihe timing sequence pulses are generated internally and control each function selection and detection chronologically. The device herein contemplated may be used to sample any one of a plurality of synchros in which case flip-dop 408 feeds a pair of and gates, for each synchro input, each pair of gates is controlled by a channel selector. The sine 6 function operates in the same manner as the cosine with the folplier 410 is made positive to allow for the magnitude positive signal open switches 411:1 and 411k and shortV switches 4120l and 412k and do the reverse upon receiving a negative signal. This is done by means of Hip-flop 413. One timing sequence or pulse later, flip-flop 416 on the sine side is inverted and allproper signals are applied to the comparison loop. The conversion takes place, the input to the regi-ster is open and the octant correction matrix corrects the binary digits 500 or readout, from the register by applying required digits 501 required by Table 11 or inverting the digits.

Since error may occur when angles very close to mul tiples of 45 are sampled, a level detector 417 detects polarities and magnitudes well within the accuracy requirement of the system.

COARSE AND FINE SYNCHRO In some cases, the sine-cosine input will be furnished by a coarse and a line device, the fine device acting as an angle. vernier within the coarse device. As long as the sectors of the coarse synchro or input device can fit into the binary scheme, no problem will be encountered. In some cases, the coarse input device or synchro may be divided into steps, or 36 sectors in 360. This does not correspond to a power of 2. Consequently, the scale factor of the switch-resistor network must be modified and the sector correction is no longer simply a subtraction from or addition to a power of 2.

FIGURE 13 illustrates in block diagram the conversion system used when the coarse angle indicator or synchro is not divided into sectors corresponding to a power of 2. To prevent ambiguity between the coarse and fine register readout, two extra digits are provided in the coarse network. These correspond to the two most significant digits of the fine synchro register readout. The two pairs of digits are compared and corrections made accordingly to the coarse synchro register. If the corresponding digits compare identically, no correction is necessary. Table 12 indicates the action necessary if they do not compare.

Table 12 Subtract 1 Yes=l No= 0 Add 1 Yes: 1 No 0 Coarse digits 21o Fine digits 210 Syn chro Synchro 29 20 An addition of +1 to the register reading requires that the binary number 000 000 001 be added to the register reading. The subtraction of -1 is obtained by adding binary number 111 111 111 to the register reading. But before the ambiguity operation can be performed, the coarse synchro register reading must be corrected for each 45 octant. Table 13 indicates the correction operation required for each sector. The addition of 90, 180 or 270 requires that the binaryl numbers 'shown in the table be added to the register reading. To perform the subtraction operation, addition is used as follows:

I (Equation A) where C is the binary numberfor 180, 270 or 360 and 0' is the number in the register readout. We can define 0i (or 0 inverted) as (Equation C) therefore by rearranging Equation B, We

obtain 0=-0 inverted -l-29-1 (EquationD) and substituting Equation C into Equation A:

But for a 29 system, 29 does not contribute into the system. (Equation E) Vsothat 0:.-C-l-l-i-0i (and 29 can be dropped Thus, all constants are simply summed into a standard adder.

Table 13 indicated the operation in each sector.

The operation sequence of the coarse synchro conversion will be:

(1) Perform conversion identical to fine synchro conversion.

invert 0 and add 100100001.

The error curve readout obtainable` from a device of the type described is plotted in FIGURE 14. As shown in the error curve, it is possible to pull up the centers of the curve by pulling up the ends for each segment. This is done by using resistors having a total resistance value slightly less than the value corresponding to the cotangent in each of the coarse digit branches, i.e., branches 26 and 27. This is particularly necessary in segment num-ber 2 between 11`11 and 221/2 The use of the resistance values described in the specification rather than the theoretically obtained values pulled up the sides of the segment number 2 curve and consequently pulled up the center of the curve.

In describing the invention herein contemplated, emphasis has been laid on a description of the overall system rather than on the individual components of the system. In practice, the angle readout can be provided in a few microseconds. To accomplish this, it isv preferable to use the transistor switch arrangement described in our copending U.S. patent application Serial No. 2670 filed on'l'anuary, 15, 1960. The buffer amplifiers are A.C. wide band amplifiers receiving as an input a gated pulse at a 40 kc. rate. The amplifier, after a period of a few microseconds presents the amplified signal on its output and this output must remain proportional to its input within the error permitted in the system over one sampling period. With a sampling period of about 15 microseconds, the 10W frequency cutoff need only be in the order of 50 c.p.s. to prevent droop with the accuracy demanded bythe system. A conventional A.-C. amplifier with high feedback will meet these requirements. Little has been said as to the readout means since readout means are well known in the art. The readout is actuated by the register and can be displayed in a visible readout or can be fed to conversion means to convert the binary reading to a decimal reading. The comparator is known in the art Iand mentioned in The International Dictionary of Physics and Electronics, D. Van Nostrand Cornpany, Inc., 1956, page 1621 and Millman and Taub, Pulse and Digital Circuits McGraw Hill, 1956 edition, page 483.

The arrangement herein described provides the output desired by means of-a ratio effect. This is particularly advantageous since line voltage errors are thus canceled out.

It is to be observed therefore that the present invention contemplates a device which provides for a digital value anglogous to an angle sensed by a sine-cosine source, e.g., a resolver or synchro 99, and comprises, in combination, a coarse network 11 into which is fed one of said sine-cosine outputs, having a plurality of parallel branches providing base binary values corresponding to the tangentcotangent of a plurality of base angular binary positions in the to 45 circle octant; a fine network 12 associated with said coarse network having a plurality of binary branches providing iine binary values between said base binary values; an attenuation network 13 interrelating said coarse and tine network values; overload switch means for said branches so biased as to permit current flow through a branch when the potential to the branch controlled by said switch towards the source is higher than the potential to the branch from the sorce; a comparator 14 into which is fed the other of the sine-cosine outputs from said source and the output from said network a shift register 300 actuated by the output from said comparator 14; a register 200 actuated by said shift register 300 controlling the overload switch means, providing angle binary values analogous to tangent-cotangent values of between 0 and 45 magnitude detection means 402 adapted to detect whether the cosine is greater than the sine; polarity detection means 401a and 401'b adapted to detect the polarity of the sine and cosine; and phase detection means 418 adapted to determine the phase of the cosine voltage to the input voltage, octant correction means 403 receiving the outputs magnitude, polarity and phase detection means, adaptedto adjust said register tangent-cotangent value to provide a digital value analagous to an angle between 0 and 360.

The invention herein described may also be used to provide a monotonic increasing function which can be treated as a plurality of straight line base points P1, P2, Pn 1, Pn. The base points intermediate the ends, i.e., points P2, P3, P11 2, Pn 1, can be represented by base resistor branches. The values between two succeeding points being represented by linearly increasing fine resistor branches. The interrelationship and the series resistance Rs between the base and line branches to provide desired attenuation between the two highest points of the function P11 and Pn 1 being provided by the formula R.,-all R Furthermore, as is readily apparent it is immaterial whether the function used are sine values or cosine values on the one hand and tangent values or cotangent values on the other hand, the proper function to use being readily understood by those skilled in the art. -For this reason, in describing the invention, the terms sine-cosine; and tangent-cotangent have been used and by these hyphenated words, we .simply means whichever of the two function required to perform the operation required in connection with the particular circuitry used. When not hy-phenated these words mean the functions specied. Also, the terms binary, and binary value as used herein refer to values shown in Table 1, or a similar table devised for the type of device herein contemplated but having either a greater or a lesser accuracy than the device herein described. In Table l, the binary value of 211 has arbitrarily assigned to 360. If a coarse and tine synchro are used, there would not be too great a loss of accuracy if the binary Value of 21 were assigned to 360.

Finally, in describing the present invention, use has been made of a tangent function to best illustrate the concept involved. Those skilled in the art will readily see that tan: Sin 0 (where K=90) tion and could be used as the basis for a circuit similar to the network illustrated in the drawing. This may best be understood by looking at FIGURE l0 showing two identical sinusoidal curves ninety degrees apart. To obtain the tangent-cotangent, the instantaneous value on one curve is divided by the corresponding value on the other curve. If one curve is moved laterally with respect to the other, and the instantaneous values were divided, the resultant function could likewise be used for the purpose of the present invention. In the last analysis' therefore, ythe invention provides an arrangement for converting angular relationship into digital units corresponding thereto, utilizing a rotatable source furnishing two outputs which are electrical values of the same kind, e.g., volts or amperes with respect to the angular position of said rotatable source which values may be represented as sin 6 and sin (-l-k), where 0 is the angular position of said source with respect to a base line and k is a constant angular value other than a value where sin 0 is Vabout equal to sin (0A-k), i.e., where the two curves of FIGURE 10 will coincide. One of the outputs of said source is fed into a network adapted to furnish electrical digital values corresponding to the function This network has overload switch means allowing only electrical values therethrough which are less than the values flowing thereto. The other output of said source is fed into comparator means into which is also fed the output from said network. Digital means responsive to said network provides digits corresponding to the electrical values passing through said network.

Although the present invention has been described in conjunction with preferred embodiments, it is to be understood that modifications and variations may be resorted to without departing from the spirit and scope of the invention as those skilled in the art will readily understand. Such modifications and variations are considered to be within the purview and scope of the invention and appended claims.

We claim:

1. A network arrangement to provide an electric current corresponding to a monotonic changing function by treating the function as a plurality of straight line base points P0, P1, P2 Pn 1, Pn where P0, P1, P2 respectively represent the zero value of the funct-ion, the first point, and the second point, and P 1 and Pn respectively represent the point before the highest vvalue' of the function and the highest value of the function, said arrangement comprising in combination:

a plurality of parallel base resistor branches supplying the values of the succeeding points: P1, P2 Pmi, `other than points P and Pn, switch means in each branch to enable each branch into the circuit or to shunt it out of the circuit;

a plurality of linearly increasing parallel fine resistor branches corresponding to increasing bit values between any succeeding points in parallel with said |base branches, switch means in each branch to enable each branch into the circuit or shunt it out of the circuit;

an attenuator coupled to each one of said base branches providing the incremental slope interrelating said one base point and next succeeding higher base point, the attenuation between the two highest points of the function, Pn 1 and Pn, being provided by a series resistance Rs disposed between the base and ine resistor branches, the value ofRS being provided by the formula t-he attenuation resistance value Rp between any two selected succeeding base points other than said two highest points Ibeing provided by the formula I (Rs'i-R where dI is the difference in current to be accounted for by the total of all the fine resistor branches between said selected two succeeding points, R is the total resistance value of all the fine resistance branches, and E is any input voltage to the network, said attenuation value Rp being s-hunted lout of the circuit upon the enabling of the switch means of the corresponding base resistor; and,

means to sequentially operate said switch means to enable each of said base and fine resistor branches or to Yshunt it out of the circuit.

2. A network arrangement to provide an electric current corresponding to a monotonie changing function by treating the function Vas a plurality of straight line base points P0, P1, P2 Pn 1, Rn Where P0, P1, P2 respectively represent the zero value of the function, the rst point, and the second point, and Pn 1 and Pn respectively represent the point before the highest value of the function and the highest value of the function, said arrangement comprising in combination:

a plurality of parallel lbase resistors branc-hes supplying the values of the succeeding points: P1, P2 Pn 1, other ythan points P0 and Pn, the ohmic values of the resistors in said base resistor branches being incremented in the binary system, the ohmic value Rpm1 of the resistor branch being given to point Pn 1 having the lowest binary value, the ohmic value Rpn 2 of the resistor branch for point Pm2 being equal to 2 Rn 1; and, the ohmic value R21 of the resistor branch for point P1 being equal to o .ZXRP2 the ohmic value of the resistor branch for point P2, switch means in each branch to enable each branch into the circuit or to chunt it out of the circuit;

u plurality of linearly increasing parallel fine resistor Ibranches corresponding to Yincreasing bit values between any succeeding points in parallel with said base branches, switch means in each branch to enable each branch into the circuit or shunt it out of the circuit;

an attenuator coupled to each 'one of said base branches providing the incrementalV slope interrelating said one base point and the next succeeding higher base point, the attenuation between the two highest points of the function, P 1 and Pn, being provided by a series resistance Rs disposed between the base and fine resistor branches, the value of Rs being provided by the formula E R,- dI R the attenuation resistance value Rp between any two selected succeeding base points other than said two highest points being provided by the formula l RD=E R R,

where dl is the difference in current to be accounted for by the total of all t-he fine resistor branches between said selected two succeeding points, R is the total resistance'value of all the iine resistance branches, andE is any input voltage to the network, said attenuation value Rp being shunted out of t-he circuit upon the enabling of the switch means of thecorresponding base resistor; and,

means t-o sequentially operate said switch means to enable each of said base and ne resistor branches or to shunt it out of the circuit.

3. A'network arrangement to provide an electric current corresponding to a monotonie changing function by treating the function as a plurality of straight line base Points P0, P1, P2 Pn 1, Pn Where P0, P1, P2 Iespectively represent the zero value of the function the first point, and the second point, and 1) 1 and Pn respectively represent the point before the highest value of the function and the highest value ofthe function, said arrangement comprising in combination:

a plurality of parallel base resistor branches supplying the values of the succeeding points: P1, P2 Pn 1, other than points P0 and Pn, the ohmic values o f the resistors in said base resistor branches being incremented in the binary system, the ohmic value Rpml of the resistor branch being given to point Pn 1 'having the lowest binary value, the ohmic value Rpn 2 of the resistor branch for point Pn 2 being equal to ZXRPIH; and, the ohmic Value RF1 of the resistor branch for point P1 being equal to 2 RP2 the ohmic value of the resistor branch for point P2, switch means in each branch to enable each branch into the circuit or to shunt it out of the circuit;

a plurality of linearly increasing parallel fine resistor branches corresponding to increasing bit values between any succeeding points in parallel with said base branches, there being mi-1 iine branches increimented, in the binary system as branches having values 20, 21, 22, 2111-1, 2m, the highest binary `current value being across the branch having the lowest resistance value of Rf ohms supplying a current of 2m amperes, and the resistance value of any other fine branch n being equal to 2mn Rf where n is any of the binary powers of 2 between 0 and m, including bothY terms, switch means in each branch to enable each Ibranch into the circuit orV shunt it out of the circuit;

an attenuator coupled to each one of said base branches providing the incremental slope interrelating said one base point and the next succeeding higher base point, the attenuation between the two highest points of the function, Pn 1 and Pn, being provided by a series resistance Rs disposed between the base and fine resistor branches, the value of Rs being provided by the formula the attenuation resistance value Rp between any 21 two selected succeeding base points other than said two highest points being provided by the formula where dI is the difference in current t-o be accounted for by the total -of all the -ne resistor branches between said selected two succeeding points, R is the total resistance value of all the ne resistance branches, and E is any input voltage to the network, said attenuation value Rp being shunt-ed out of the circuit upon the enabling ofthe switch means of the corresponding base resistor; and, means to sequentially operate said switch means to enable each of said base and line resistor branches or to shunt it out of t-he circuit.

4. A device `as claimed in claim 3 wherein each of said coarse and fine branches has two series resistors, the Values of said resistors being RbH and Rb (l-H), where Rb is the total resistance of the branch and H is the fractional value of one of the resistors in the branch to the total resistance of the branch; said switch means being between said two resistors.

References Cited by the Examiner UNITED STATES PATENTS 2,434,155 1/ 1948 Haynes. 2,656,102 10/1953 Redheffer 235-186 X 3,027,082 3/ 1962 S-hih Chieh Chao. 3,063,637 11/1962 Buuhans 235-197 X 3,080,555 3/1963 Vadus et al. 235-197 X 3,088,671 f 5/1963 Chase 235-197 X OTHER REFERENCES Hofheimer et al.: Digital-Analog Function Generators.

In IRE Transactions on Instrumentation, pages 111-117,

June 1958.

MALCON A. MORRISON, Primary Examiner.

S. C. CORWIN, I. KESCHNER, Assistant Examiners. 

1. A NETWORK ARRANGEMENT TO PROVIDE AN ELECTRIC CURRENT CORRESPONDING TO A MONOTONIC CHANGING FUNCTION BY TREATING THE FUNCTION AS A PLURALTIY OF STRAIGHT LINE BASE POINTS P0, P1, P2 ... PN-1, PN WHERE P0, P1, P2 RESEPECTIVELY REPRESENT THE ZERO POINT, AND THE FUNCTION, THE FIRST POINT, AND THE SECOND POINT, AND PN-1 AND PN RE SPECTIVELY REPRESENT THE POINT BEFORE THE HIGHEST VALUE OF THE FUNCTION AND THE HIGHEST VALUE OF THE FUNCTION, SAID ARRANGEMENT COMPRISING IN COMBINATION: A PLURALITY OF PARALLEL BASE RESISTOR BRANCHES SUPPLYING THE VALUES OF THE SUCCEEDING POINTS: P1, P2 ... PN-1, OTHER THAN POINT P0 AND PN, SWITCH MEANS IN EACH BRANCH TO ENABLE EACH BRANCH INTO THE CIRCUIT OR TO SHUNT IT OUT OF THE CIRCUIT; A PLURALITY OF LINEARLY INCREASING PARALLEL FINE RESISTOR BRANCES CORRESPONDING TO INCREASING BIT VALUES BETWEEN ANY SUCCEEDING POINTS IN PARALLEL WITH SAID BASE BRANCHES, SWITCH MEANS IN EACH BRANC TO ENABLE EACH BRANCH INTO THE CIRCUIT OR SHUNT IT OUT OF THE CIRCUIT; AN ATTENUATOR COUPLED TO EACH ONE OF SAID BASE BRANCHES PROVIDING THE INCREMENTAL SLOPE INTERRELATING SAID ONE BASE POINT AND NEXT SUCCEEDING HIGHER BASE POINT, THE ATTENUATION BETWEEN THE TWO HIGHEST BASE POINT, THE FUNCTION, PN-1 AND PN, BEING PROVIDED BY A SERIES RESISTANCE RS DISPOSED BETWEEN THE BASE AND FINE RESISTOR BRANCES, THE VALE OF RS BEING PROVIDED BY THE FORMULA 